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Remarks on the one-point density of Hele-Shaw $β$-ensembles
Yacin Ameur, Erik Troedsson · 2024-02-21 · via math.PR updates on arXiv.org

In this note we prove equicontinuity for the family of one-point densities with respect to a two-dimensional Coulomb gas at an inverse temperature $β\ge 1/2$ confined by an external potential of Hele-Shaw (or quasi-harmonic) type. As a consequence, subsequential limiting Lipschitz continuous densities are defined on the microscopic scale. There are several additional results, for example comparing the one-point density with the thermal equilibrium density.

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